Global well‐posedness of space‐time fractional diffusion equation with Rockland operator on graded lie group
Year: 2024
Type: article
Abstract: In this article, we examine the general space‐time fractional diffusion equation for left‐invariant hypoelliptic homogeneous operators on graded Lie groups. Our study covers important examples such as the time fractional diffusion equation, the space‐time fractional diffusion equation when diffusion is under the influence of sub‐Laplacian on the Heisenberg group, or general stratified Lie groups. We establish the global well‐posedness of the Cauchy problem for the general space‐time fractional diffusion equation of the Rockland operator on a graded Lie group in the associated Sobolev spaces and also develop some regularity estimates for it.
DOI: 10.1002/mma.10583
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funders: Department of Science and Technology, Ministry of Science and Technology, India, Fonds Wetenschappelijk Onderzoek, Universiteit Gent, Indian Institute of Technology Delhi, Engineering and Physical Sciences Research Council, Science and Engineering Research Board, Bijzonder Onderzoeksfonds UGent
Awards: G1083792743, G1370395892, G1525296937, Regularity in affiliated von Neumann algebras and applications to partial differential equations, G3130771253, Analysis and Partial Differential Equations (APDE), G3624573134, G3980025746, G4241671331, G4733659820, G6715076113, G6787693879, G7415185036, Hyperbolic problems with discontinuous coefficients
OpenAlex ID: W4404249603